Abstract

Multiple light scattering can be suppressed by slightly tilting two single-mode fibers viewing the same sample volume. The cross-correlation function of the two signals shows more or less contributions from single scattering, depending on the tilt angle. We show experimental results for polystyrene spheres at a scattering angle of 90°. The measured size, intercept, and second cumulant for different tilt angles demonstrate the practicality of this technique. Both polarization components show multiple-scattering contributions, but only the parallel component contains single scattering.

© 1997 Optical Society of America

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References

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  1. B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).
  2. D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
    [CrossRef] [PubMed]
  3. D. A. Weitz, D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light Scattering: The Method and Some Applications, W. Brown, ed. (Oxford U. Press, New York, 1993), pp. 652–720.
  4. R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
    [CrossRef]
  5. H. Wiese, D. J. Horn, “Single-mode fibers in fiber-optic quasielastic light scattering: a study of the dynamics of concentrated latex suspensions,” J. Chem. Phys. 94, 6429–6443 (1991).
    [CrossRef]
  6. P. N. Segrè, W. Van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-color dynamic light-scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
    [CrossRef]
  7. F. Stieber, W. Richtering, “Fiber-optic-dynamic-light-scattering and two-color-cross-correlation studies of turbid, concentrated, sterically stabilized polystyrene latex,” Langmuir 11, 4724–4727 (1995).
    [CrossRef]
  8. G. D. J. Phillies, “Suppression of multiple-scattering effects in quasielastic-light-scattering spectroscopy by homodyne cross-correlation techniques,” J. Chem. Phys. 74, 260–262 (1981).
    [CrossRef]
  9. G. D. J. Phillies, “Experimental demonstration of multiple-scattering suppression in quasielastic-light-scattering spectroscopy by homodyne coincidence techniques,” Phys. Rev. A 24, 1939–1943 (1981).
    [CrossRef]
  10. J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 79, 1658–1663 (1983).
    [CrossRef]
  11. R. G. W. Brown, “Dynamic light scattering using mono-mode optical fibers,” Appl. Opt. 26, 4846–4851 (1987).
    [CrossRef] [PubMed]
  12. J. Rička, “Dynamic light scattering with single-mode and multimode receivers,” Appl. Opt. 32, 2860–2875 (1993).
    [CrossRef] [PubMed]
  13. W. V. Meyer, D. S. Cannell, A. E. Smart, T. W. Taylor, P. Tin, “Multiple-scattering suppression by cross correlation,” Appl. Opt. 36, 7551–7558 (1997).
    [CrossRef]
  14. J. A. Lock, “Role of multiple scattering in cross-correlated light scattering with a single laser beam,” Appl. Opt. 36, 7559–7570 (1997).
    [CrossRef]
  15. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1994), p. 428.
  16. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1994), p. 188ff.

1997 (2)

1995 (2)

P. N. Segrè, W. Van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-color dynamic light-scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
[CrossRef]

F. Stieber, W. Richtering, “Fiber-optic-dynamic-light-scattering and two-color-cross-correlation studies of turbid, concentrated, sterically stabilized polystyrene latex,” Langmuir 11, 4724–4727 (1995).
[CrossRef]

1994 (1)

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

1993 (1)

1991 (2)

H. Wiese, D. J. Horn, “Single-mode fibers in fiber-optic quasielastic light scattering: a study of the dynamics of concentrated latex suspensions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
[CrossRef] [PubMed]

1987 (1)

1983 (1)

J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 79, 1658–1663 (1983).
[CrossRef]

1981 (2)

G. D. J. Phillies, “Suppression of multiple-scattering effects in quasielastic-light-scattering spectroscopy by homodyne cross-correlation techniques,” J. Chem. Phys. 74, 260–262 (1981).
[CrossRef]

G. D. J. Phillies, “Experimental demonstration of multiple-scattering suppression in quasielastic-light-scattering spectroscopy by homodyne coincidence techniques,” Phys. Rev. A 24, 1939–1943 (1981).
[CrossRef]

Ackerson, B. J.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

Berne, B. J.

B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

Brown, R. G. W.

Cannell, D. S.

de Kruif, C. G.

J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 79, 1658–1663 (1983).
[CrossRef]

Dhont, J. K. G.

J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 79, 1658–1663 (1983).
[CrossRef]

Dorri-Nowkoorani, F.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

Dougherty, R. L.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

Durian, D. J.

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
[CrossRef] [PubMed]

Horn, D. J.

H. Wiese, D. J. Horn, “Single-mode fibers in fiber-optic quasielastic light scattering: a study of the dynamics of concentrated latex suspensions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

Lock, J. A.

Mandel, L.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1994), p. 188ff.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1994), p. 428.

Meyer, W. V.

Nobbmann, U.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

Pecora, R.

B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

Peters, W.

P. N. Segrè, W. Van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-color dynamic light-scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
[CrossRef]

Phillies, G. D. J.

G. D. J. Phillies, “Suppression of multiple-scattering effects in quasielastic-light-scattering spectroscopy by homodyne cross-correlation techniques,” J. Chem. Phys. 74, 260–262 (1981).
[CrossRef]

G. D. J. Phillies, “Experimental demonstration of multiple-scattering suppression in quasielastic-light-scattering spectroscopy by homodyne coincidence techniques,” Phys. Rev. A 24, 1939–1943 (1981).
[CrossRef]

Pine, D. J.

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
[CrossRef] [PubMed]

D. A. Weitz, D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light Scattering: The Method and Some Applications, W. Brown, ed. (Oxford U. Press, New York, 1993), pp. 652–720.

Pusey, P. N.

P. N. Segrè, W. Van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-color dynamic light-scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
[CrossRef]

Reguigui, N. M.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

Richtering, W.

F. Stieber, W. Richtering, “Fiber-optic-dynamic-light-scattering and two-color-cross-correlation studies of turbid, concentrated, sterically stabilized polystyrene latex,” Langmuir 11, 4724–4727 (1995).
[CrossRef]

Ricka, J.

Schätzel, K.

P. N. Segrè, W. Van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-color dynamic light-scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
[CrossRef]

Segrè, P. N.

P. N. Segrè, W. Van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-color dynamic light-scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
[CrossRef]

Smart, A. E.

Stieber, F.

F. Stieber, W. Richtering, “Fiber-optic-dynamic-light-scattering and two-color-cross-correlation studies of turbid, concentrated, sterically stabilized polystyrene latex,” Langmuir 11, 4724–4727 (1995).
[CrossRef]

Taylor, T. W.

Tin, P.

Van Megen, W.

P. N. Segrè, W. Van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-color dynamic light-scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
[CrossRef]

Weitz, D. A.

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
[CrossRef] [PubMed]

D. A. Weitz, D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light Scattering: The Method and Some Applications, W. Brown, ed. (Oxford U. Press, New York, 1993), pp. 652–720.

Wiese, H.

H. Wiese, D. J. Horn, “Single-mode fibers in fiber-optic quasielastic light scattering: a study of the dynamics of concentrated latex suspensions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

Wolf, E.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1994), p. 188ff.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1994), p. 428.

Appl. Opt. (4)

J. Chem. Phys. (3)

J. K. G. Dhont, C. G. de Kruif, “Scattered light intensity cross correlation. I. Theory,” J. Chem. Phys. 79, 1658–1663 (1983).
[CrossRef]

H. Wiese, D. J. Horn, “Single-mode fibers in fiber-optic quasielastic light scattering: a study of the dynamics of concentrated latex suspensions,” J. Chem. Phys. 94, 6429–6443 (1991).
[CrossRef]

G. D. J. Phillies, “Suppression of multiple-scattering effects in quasielastic-light-scattering spectroscopy by homodyne cross-correlation techniques,” J. Chem. Phys. 74, 260–262 (1981).
[CrossRef]

J. Mod. Opt. (1)

P. N. Segrè, W. Van Megen, P. N. Pusey, K. Schätzel, W. Peters, “Two-color dynamic light-scattering,” J. Mod. Opt. 42, 1929–1952 (1995).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, U. Nobbmann, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

Langmuir (1)

F. Stieber, W. Richtering, “Fiber-optic-dynamic-light-scattering and two-color-cross-correlation studies of turbid, concentrated, sterically stabilized polystyrene latex,” Langmuir 11, 4724–4727 (1995).
[CrossRef]

Phys. Rev. A (1)

G. D. J. Phillies, “Experimental demonstration of multiple-scattering suppression in quasielastic-light-scattering spectroscopy by homodyne coincidence techniques,” Phys. Rev. A 24, 1939–1943 (1981).
[CrossRef]

Science (1)

D. J. Durian, D. A. Weitz, D. J. Pine, “Multiple light-scattering probes of foam structure and dynamics,” Science 252, 686–688 (1991).
[CrossRef] [PubMed]

Other (4)

D. A. Weitz, D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light Scattering: The Method and Some Applications, W. Brown, ed. (Oxford U. Press, New York, 1993), pp. 652–720.

B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1994), p. 428.

L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1994), p. 188ff.

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Figures (5)

Fig. 1
Fig. 1

Experimental setup for the fiber multiple-scattering suppression. The two detectors are in the xz plane and each form an (extremely) small (mrad) angle θ/2 with the x axis. The input laser is in the xy plane at an angle ϕ (traditional scattering angle) with the x axis.

Fig. 2
Fig. 2

Intercept versus angular tilt for the cross correlation of a multiple-scattering sample. The curve is the expected behavior for the sample parameters with an assumed ratio (A:B) of multiple-to-single scattering of 1:600 (0.107-µm polystyrene, Φ = 0.0015).

Fig. 3
Fig. 3

Intercept versus angular tilt for the two polarizations of a multiple-scattering sample. The filled circles are the fits to the cross-correlation functions of the parallel polarization component. The open circles are for the perpendicular polarization data. The curves are calculated with an assumed ratio (A:B) of multiple-to-single scattering of 1:700 for the parallel and 1:0 for the perpendicular component (0.107-µm polystyrene, Φ = 0.0025).

Fig. 4
Fig. 4

Particle size (in nanometers) versus angular tilt for the two polarizations of a non-single-scattering sample. The filled circles are the radius obtained from a fit to the cross-correlation function of the parallel polarization component. The open circles are fits to the perpendicular polarization data. The cross-hatched area is the expected size for single scattering. (0.107-µm polystyrene, Φ = 0.0025).

Fig. 5
Fig. 5

Normalized second cumulant versus angular tilt for the two polarizations of a non-single-scattering sample. The filled circles are the fits to the cross-correlation function of the parallel polarization component. The open circles are for the perpendicular polarization data. The cross-hatched area represents the single-scattering expectation for this sample (0.107-µm polystyrene, Φ = 0.0025).

Equations (11)

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Ir1, t1Ir2, t2=Ir1, t1Ir2, t2×1+γr1, r2, t1-t22.
γr1, r2, 0=Irexp-iks1-s2·rd3r/Ird3r
I1x, y, z=exp-αy2+z cosθ/2-x sinθ/22.
I2x, y, z=exp-αy2+z cosθ/2+x sinθ/22.
Issx, y, z=B exp-βz2+x sinϕ+y cosϕ2,
Igcx, y, z=exp-2δx2+y2+z2.
γr1, r2, 0=exp-i2kz sinθ/2×I1x, y, zI2x, y, zIgcx, y, z×A+Issx, y, zd3r  I1x, y, z×I2x, y, zIgcx, y, zA+Issx, y, zd3r.
γθ=A exp-q2θ2/8αα2αθ2/4+δ1/2+2B exp-q2θ2/4ββ sin ϕ α×A/αδ+2B/βα sin ϕ.
G2τ=1+γθ2G1τ2.
G2τ=1+γ2 exp-2uτ+2uτ2
u=Dq2=kBT6πηr4πnλsinθ22.

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